Optimizing stakes in simultaneous bets

Robbert Fokkink; Ludolf Meester; Christos Pelekis

doi:10.30757/ALEA.v20-07

Optimizing stakes in simultaneous bets

Robbert Fokkink^*, Ludolf Meester, Christos Pelekis

^*Corresponding author for this work

Applied Probability

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

We want to find the convex combination S of iid Bernoulli random variables that maximizes P(S ≥ t) for a given threshold t. Endre Csóka conjectured that such an S is an average if t ≥ p, where p is the success probability of the Bernoulli random variables. We prove this conjecture for a range of p and t

Original language	English
Pages (from-to)	153-165
Number of pages	13
Journal	Alea (Rio de Janeiro)
Volume	20
Issue number	1
DOIs	https://doi.org/10.30757/ALEA.v20-07
Publication status	Published - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

bold play
intersecting family
small deviations
stochastic inequality

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20-07Final published version, 540 KB

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AU - Meester, Ludolf

AU - Pelekis, Christos

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N2 - We want to find the convex combination S of iid Bernoulli random variables that maximizes P(S ≥ t) for a given threshold t. Endre Csóka conjectured that such an S is an average if t ≥ p, where p is the success probability of the Bernoulli random variables. We prove this conjecture for a range of p and t

AB - We want to find the convex combination S of iid Bernoulli random variables that maximizes P(S ≥ t) for a given threshold t. Endre Csóka conjectured that such an S is an average if t ≥ p, where p is the success probability of the Bernoulli random variables. We prove this conjecture for a range of p and t

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KW - intersecting family

KW - small deviations

KW - stochastic inequality

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JF - Alea (Rio de Janeiro)

IS - 1

ER -

Optimizing stakes in simultaneous bets

Abstract

Bibliographical note

Keywords

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